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219 lines
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219 lines
7.9 KiB
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=============================================
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Tuto I: One- and two-e integrals (20 minutes)
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=============================================
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Requirements
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------------
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1) You know how to create an |EZFIO| file and run calculations with |QP| (check the tuto: `<https://quantumpackage.github.io/qp2/post/hartree-fock/>`_),
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2) You have an |EZFIO| file with MOs created (with the :ref:`scf` executable for instance). As we are going to print out some integrals, don't take a too large system/basis (Ex: H2, cc-pVDZ is ok :)
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3) You made an qp set_file YOUR_EZFIO_FILE_FOR_H2 in order to work on that ezfio folder.
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4) You have READ the :file:`qp2/plugins/README.rst` file to HAVE THE **VOCABULARY**.
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Our goals:
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----------
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We want to create a plugin to do the following things:
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1) print out one- and two-electron integrals on the AO/MO basis,
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2) creates two providers which manipulate these objects,
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3) print out these providers.
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I) Getting started: creating the plugin
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---------------------------------------
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We will go step-by-step through these plugins.
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We will create a plugin named "plugin_I", and its location will be in "tuto_plugins".
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Therefore to create the plugin, we do:
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.. code:: bash
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qp plugins create -n plugin_I -r tuto_plugins
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Then do an "ls" in qp2/plugins/tuto_plugins/ and you will find a directory called "plugin_I".
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In that directory you will find:
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1) a :file:`NEED` file that will eventually contain all the other modules/plugins needed by our "plugin_I",
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2) a :file:`README.rst` file that you can and **SHOULD** modify in order to **DOCUMENT** what is doing the plugin,
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3) a :file:`plugin_I.irp.f` file that is a program to be compiled and just printing "Hello world"
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II) Specifying the dependencies
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-------------------------------
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The next step is to know what are the other modules/plugins that we need to do what we want.
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We need here
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a) the one-electron integrals on the AO basis, which are computed in :file:`qp2/src/ao_one_e_ints/`
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b) the one-electron integrals on the MO basis, which are computed in :file:`qp2/src/mo_one_e_ints/`
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c) the two-electron integrals on the AO basis, which are computed in :file:`qp2/src/ao_two_e_ints/`
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d) the two-electron integrals on the MO basis, which are computed in :file:`qp2/src/mo_two_e_ints/`
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Therefore, we will need the following four modules:
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a) ao_one_e_ints
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b) mo_one_e_ints
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c) ao_two_e_ints
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d) mo_two_e_ints
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You can then create the following "NEED" file by executing the following command
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.. code:: bash
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cat <<EOF > NEED
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ao_one_e_ints
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mo_one_e_ints
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ao_two_e_ints
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mo_two_e_ints
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EOF
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II) Installing the plugin
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-------------------------
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Now that we have specified the various depenencies we need now to INSTALL the plugin, which means to create the equivalent of a Makefile for the compilation.
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To do it we simply do
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.. code:: bash
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qp plugins install plugin_I
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III) Compiling the void plugin
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------------------------------
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It is customary to compile first your "void" plugin, void in the sense that it does not contain anything else than the program printing "Hello world".
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To do so, just go in the plugin and execute the following command
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.. code:: bash
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ninja
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It does a lot of stuffs, but it must conclude with something like
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.. code:: bash
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make: Leaving directory 'SOME_PATH_TOWARD_YOUR_QP2_DIRECTORY/qp2/ocaml'
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Since that it has compiled, an executable "plugin_I" has been created.
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Also, if you make "ls" in the "plugin_I" you will notice that many symbolink links have been created, and among which the four modules that you included in the NEED file.
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All the other modules (Ex::ref:`module_ao_basis`, :ref:`module_utils`) are here because they are need by some of the four modules that you need.
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The variables that we need are
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:data:`ao_one_e_integrals`
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:data:`mo_one_e_integrals`
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You can check them with
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.. code:: bash
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irpman ao_one_e_integrals
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.. code:: bash
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irpman mo_one_e_integrals
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in order to get some information on where they are created, and many more information.
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We will now create an executable such that it prints out the integrals.
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IV) Printing out the one-electron integrals
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--------------------------------------------
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We will now create a program that will print out the one-electron integrals on the AO and MO basis.
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You can then copy the file :file:`qp2/plugins/tuto_plugins/tuto_I/print_one_e_h.irp.f` in your plugin.
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In this file you will see that we simply browse the two arrays :data:`ao_one_e_integrals` and :data:`mo_one_e_integrals`, which are the providers and we browse them until either :data:`ao_num` or :data:`mo_num` which are also providers representing the number of AOs or MOs.
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.. seealso::
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You can check these variables with :command:`irpman` !
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If you recompile using |ninja| as before, and another executable has been created "print_one_e_h".
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Then, you can run the program on the ezfio file by doing
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.. code:: bash
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qp run print_one_e_h
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and will print out the data you need :)
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By the way, as the file :file:`plugin_I.irp.f` contains nothing but a "Hello world" print, you can simply remove it if you want.
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V) Printing out the two-electron integrals
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------------------------------------------
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We will now create a file that prints out the two-electron integrals in the AO and MO basis.
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These can be accessed with the following subroutines :
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1- :c:func:`get_ao_two_e_integral` for the AO basis
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2- :c:func:`get_two_e_integral` for the MO basis
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.. seealso::
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check them with irpman !
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To print the two-electron integrals, you can copy the file :file:`qp2/plugins/tuto_plugins/tuto_I/print_two_e_h.irp.f` in your plugin and recompile with |ninja|.
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Then just run the program
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.. code:: bash
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qp run print_two_e_h
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and it will print all the things you want :)
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VI) Creating new providers and a program to print them
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------------------------------------------------------
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We will now create new providers that manipulates the objects that we just printed.
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As an example, we will compute the trace of the one electron integrals in the AO and MO basis.
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In the file :file:`qp2/plugins/tuto_plugins/tuto_I/traces_one_e.irp.f` you will find the several new providers among which
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1- :c:data:`trace_mo_one_e_ints` : simply the sum of the diagonal matrix element of the one-electron integrals
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2- :c:data:`trace_ao_one_e_ints` : the corresponding trace on the AO basis
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.. math::
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\text{Tr}({\bf h}{\bf S}^{-1}) = \sum_{m,n} S^{-1}_{mn} h_{mn}
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3- :c:data:`trace_ao_one_e_ints_from_mo` : the trace on the AO basis with the integrals obtained first from the MO basis
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.. math::
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\text{Tr}({\bf \tilde{h}}{\bf S}^{-1}) = \text{Tr}\big({\bf SC h}({\bf SC }^T){\bf S}^{-1}\big)
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Just copy the :file:`qp2/plugins/tuto_plugins/tuto_I/traces_one_e.irp.f` in your plugin and recompile.
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.. seealso::
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Once it has compiled, check your new providers with :command:`irpman` !
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As explained in the files :file:`qp2/plugins/tuto_plugins/tuto_I/traces_one_e.irp.f` and :file:`qp2/plugins/tuto_plugins/tuto_I/print_traces_on_e.irp.f`, :c:data:`trace_mo_one_e_ints` is equal to :c:data:`trace_ao_one_e_ints` only if the number of AO basis functions is equal to the number of MO basis functions, which means if you work with cartesian functions.
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.. seealso::
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You can check with :command:`qp create_ezfio -h` for the option to create an |EZFIO| with cartesian basis functions
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In the file :file:`qp2/plugins/tuto_plugins/tuto_I/print_traces_on_e.irp.f` you will find an example of executable that prints out the various providers.
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Copy these two files in your plugin and recompile to execute it.
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Execute the program print_traces_on_e and check for the results with
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.. code:: bash
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qp run print_traces_on_e
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The code in :file:`qp2/plugins/tuto_plugins/tuto_I/print_traces_on_e.irp.f` should be easy to read, I let the reader interpret it.
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